Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This law is applicable to the recoil of a gun.

Explanation:
The recoil of a gun occurs when a bullet is fired. When the gunpowder inside the cartridge ignites, it produces rapidly expanding gases that push the bullet forward. According to Newton's Third Law, the bullet exerts a force on the gun in the forward direction. Simultaneously, the gun exerts an equal and opposite force on the bullet in the backward direction. This backward force is what we perceive as the recoil.

The bullet and the gun are part of an isolated system, meaning there are no external forces acting on them. Therefore, the total momentum of the system remains constant. Momentum is a product of an object's mass and velocity. As the bullet is relatively small and travels at a high velocity, it carries a significant amount of momentum. When the bullet is expelled from the gun, the gun experiences an equal and opposite change in momentum, causing it to move backward.

Key Points:
- The recoil of a gun can be explained by Newton's Third Law of Motion.
- According to this law, for every action (bullet moving forward), there is an equal and opposite reaction (gun moving backward).
- The gun and bullet form an isolated system, meaning there are no external forces acting on them.
- The conservation of momentum is observed in this system, where the total momentum remains constant.
- The bullet, being small and fast, carries a significant amount of momentum, which is transferred to the gun during recoil.

In conclusion, the law of motion involved in the recoil of a gun is Newton's Third Law of Motion. This law explains how the forward motion of the bullet results in an equal and opposite backward motion of the gun.